160 Attempt to facilitate Observations of 
needle. Where this fault exists, gravity unites with magnetism in determining the 
position of equilibrium of the needle, and it will assume a direction different from that 
of the resultant of the terrestrial magnetic forces. ‘The error arising from this cause, 
it is true, is in a great degree corrected by the process of reversing the poles of 
the needle, in the usual mode of observation ; but still it cannot be said to be wholly 
removed, nor are the methods of correction altogether unobjectionable. 
These and other difficulties in the direct determination of the dip, have led to the 
occasional employment of indirect methods. ‘Thus, if the total magnetic intensity be 
known, together with its vertical or its horizontal component, the dip is readily found 
by elimination, A method founded on this principle was suggested by Lariace, and 
practised by Humsotpr and Captain Sabine. The total intensity was determined by 
noting the time of vibration of a dipping needle, oscillating in the plane of the mag- 
netic meridian ; and the vertical component was similarly obtained from the time of 
vibration of the same needle in the plane at right angles to the former: the ratio of 
these two forces is equal to the sine of the dip. Captain Sazinr has also employed 
another method derived from the same principle. The horizontal component of the 
terrestrial magnetic force was found by observing the time of vibration of the needle 
suspended horizontally : and this component, divided by the total intensity, is equal to 
the cosine of the dip. The dipping needle, however, seems to be badly adapted to 
observations of vibration. Owing to the friction of the axis, the needle is soon 
brought to rest, unless the initial arc of vibration be considerable ; and, when this is 
the case, the observer is involved in many sources of error, against which it seems dif- 
ficult to guard. 
A method similar to these in principle, but free from the objections just stated, was 
adopted many years since by Coutoms. In this method, the elements obtained by ob- 
servation were the vertical and horizontal components of the intensity, the ratio of 
which is equal to the tangent of the dip. The horizontal component was determined, 
as in the last case, by observing the number of oscillations performed in a given time 
by the needle suspended horizontally ; while the vertical component was found by 
determining the weight of a counterpoise, placed at a given distance on the southern 
arm of the needle, and sufficient to bring it to the horizontal position. ‘The moment 
of this counterpoise, or its weight multiplied by its distance from the axle, is ob- 
viously equal to the vertical component of the magnetic intensity. M. Bror considers 
this as the most accurate method that has been ever applied to the determination of 
the dip. It seems, however, open to very serious objections, which have been pointed 
out by M. Pourtier. In order to determine the horizontal component from the time 
of vibration, so that it may be comparable with the other component determined sta- 
tically, it is necessary that the moment of inertia of the needle should be known a 
priori; and that this should be, the needle must have a regular mathematical form. 
